in order to estimate the genetic parameters and comparison legendre polynomials for production traits of iranian holstein dairy cattle test-day records of first lactation cows for milk yield, fat yield, protein yield, fat percentage and protein percentage traits were used. these records collected from 2006 to 2010, by the animal breeding center of iran. the genetic parameters were estimated usi...

This work describes two efficient and useful methods for solving fractional pantograph delay equations (FPDEs) with initial boundary conditions. These depend mainly on orthogonal polynomials, which are the method of operational matrix derivative that depends Bernstein polynomials Shifted Legendre polynomials. The basic procedure this is to convert equation a system linear by using, matrices we ...

in this study test-day records of milk (kg), fat (g), and protein (g) yields, somatic cell score (scs, cells/ml) collected by animal breeding center of iran during 2007 and 2009 were used to estimate genetic parameters using random regression model. models with different order of legendre polynomials were compared using bayesian information criterion (bic).for milk, fat yield and scs genetic an...

Abstract This article adopts a novel technique to numerical solution for fractional time-delay diffusion equation with variable-order derivative (VFDDEs). As matter of fact, the (VFD) that has been used is in Caputo sense. The first step this constructive on construction using shifted Legendre–Laguerre polynomials unknown coefficients. second involves combination collocation method and operatio...

A new family of wavelets is introduced, which is associated with Legendre polynomials. These wavelets, termed spherical harmonic or Legendre wavelets, possess compact support. The method for the wavelet construction is derived from the association of ordinary second order differential equations with multiresolution filters. The low-pass filter associated to Legendre multiresolution analysis is ...

Formulae expressing explicitly the coefficients of an expansion of double Jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. Extension to expansion of triple Jacobi polynomials is given. The results for the special cases of double and triple ultraspher...

We study linear transformations $$T :\mathbb {R}[x] \rightarrow \mathbb {R}[x]$$ of the form $$T[x^n]=P_n(x)$$ where $$\{P_n(x)\}$$ is a real orthogonal polynomial system. With $$T=\sum \tfrac{Q_k(x)}{k!}D^k$$ , we seek to understand behavior transformation T by studying roots $$Q_k(x)$$ . prove four main things. First, show that only case are constant and an system when $$P_n(x)$$ shifted set ...

formulae expressing explicitly the coefficients of an expansion of double jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. extension to expansion of triple jacobi polynomials is given. the results for the special cases of double and triple ultraspher...